Combine flour, sugar, salt, baking powder and cinnamon. Stir in milk and egg until just combined. Fold in apple.
Pour oil into skillet until it is approximately 1 1/2 inches deep. Heat oil on high. Oil is ready when a little dough floats to top.
Carefully add dough to the oil in heaping teaspoons. Cook until brown, about 2 minutes, then flip. Cook another 1 to 2 minutes, until both sides are brown. Transfer briefly to paper towels to absorb excess oil, then transfer to cooling rack.
Make glaze by stirring milk and sugar together in a small bowl. Drizzle over apple fritters. Wait approximately 3 minutes for glaze to harden, then flip fritters and drizzle glaze over other side. Best served warm.